Subgroups — C₂×#13112717 #15752966

Order 3328.

830 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88043	C₂	1	2	yes	maximal
2	#13112717	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₃×#382	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
5	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
6	C₂³×#1055	—	2	2	no	—
7	C₁₃×#382	—	2	2	no	—
8	C₁₃×#382	C₄	1	2	yes	—
9	C₁₃×#382	C₂²	1	2	yes	—
10	C₂×C₁₃×#95	—	2	2	no	—
11	C₂×#88043	—	2	4	no	—
12	C₂×#88043	—	2	2	no	—
13	C₂×#88043	C₄	1	8	yes	complemented
14	C₂×#88043	C₂²	1	4	yes	—
15	C₂³×C₄×C₁₃	—	2	2	no	—
16	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂³×C₄×C₁₃	D₄	1	2	yes	—
18	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
19	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
20	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
21	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
22	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₃	D₄	1	2	yes	—
24	C₂×C₄²×C₁₃	D₄	1	2	yes	—
25	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
26	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
27	C₂²×#1055	—	2	16	no	—
28	C₂²×#1055	—	2	8	no	—
29	C₂²×#1055	—	2	4	no	—
30	C₁₃×#95	—	2	4	no	—
31	C₁₃×#95	—	2	4	no	—
32	#88043	—	2	8	no	—
33	#88043	—	2	4	no	—
34	#88043	C₂×C₄	1	8	yes	complemented
35	C₂×#1295	—	13	1	no	maximal, Sylow
36	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₃	—	2	2	no	—
38	C₂²×C₄×C₁₃	—	2	2	no	—
39	C₂²×C₄×C₁₃	—	2	8	no	—
40	C₂²×C₄×C₁₃	—	2	4	no	—
41	C₂²×C₄×C₁₃	—	4	4	no	—
42	C₂²×C₄×C₁₃	—	4	8	no	—
43	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
44	C₂²×C₄×C₁₃	C₂²⋊C₄	1	4	yes	—
45	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
46	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
48	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
49	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
51	C₁₃×C₄⋊C₄	—	4	4	no	—
52	C₁₃×C₄⋊C₄	—	4	4	no	—
53	C₄²×C₁₃	C₄²	1	2	yes	—
54	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
55	C₄²×C₁₃	C₄⋊C₄	1	4	yes	—
56	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
57	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
58	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
59	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
60	C₂×#1055	—	2	32	no	—
61	C₂×#1055	—	2	16	no	—
62	C₂×#1055	—	2	8	no	—
63	C₂²×#97	—	13	2	no	—
64	C₂×#382	D₁₃	1	1	yes	characteristic
65	#1295	—	13	4	no	—
66	C₂³×C₁₃	#95	1	2	yes	—
67	C₂³×C₁₃	#100	1	2	yes	—
68	C₂³×C₁₃	#101	1	2	yes	—
69	C₂³×C₁₃	#104	1	8	yes	—
70	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₄×C₁₃	—	2	8	no	—
72	C₂×C₄×C₁₃	—	2	8	no	—
73	C₂×C₄×C₁₃	—	2	4	no	—
74	C₂×C₄×C₁₃	—	2	4	no	—
75	C₂×C₄×C₁₃	—	2	1	no	—
76	C₂×C₄×C₁₃	—	2	1	no	—
77	C₂×C₄×C₁₃	—	2	1	no	—
78	C₂×C₄×C₁₃	—	2	1	no	—
79	C₂×C₄×C₁₃	—	2	4	no	—
80	C₂×C₄×C₁₃	—	2	4	no	—
81	C₂×C₄×C₁₃	—	4	4	no	—
82	C₂×C₄×C₁₃	—	4	8	no	—
83	C₂×C₄×C₁₃	—	8	8	no	—
84	C₂×C₄×C₁₃	#95	1	4	yes	—
85	C₂×C₄×C₁₃	#95	1	2	yes	—
86	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
87	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
88	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
89	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
90	#1055	—	2	16	no	—
91	C₂³×C₈	—	26	2	no	—
92	C₂²×C₄⋊C₄	Dic₁₃	1	2	yes	—
93	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
94	C₂×#97	—	13	8	no	—
95	C₂×#97	—	13	4	no	—
96	C₂×#97	—	26	4	no	—
97	C₂×#97	—	26	2	no	—
98	#382	—	2	2	no	—
99	#382	Dic₁₃	1	2	yes	—
100	#382	C₂×D₁₃	1	2	yes	—
101	C₂×#95	—	2	2	no	—
102	C₂²×C₁₃	#329	1	8	yes	—
103	C₂²×C₁₃	#330	1	8	yes	—
104	C₂²×C₁₃	#339	1	8	yes	—
105	C₂²×C₁₃	#343	1	4	yes	—
106	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
107	C₂²×C₁₃	C₂×#100	1	1	yes	characteristic
108	C₂²×C₁₃	C₂×#101	1	1	yes	characteristic
109	C₂²×C₁₃	C₂×#104	1	4	yes	—
110	C₄×C₁₃	—	2	2	no	—
111	C₄×C₁₃	—	2	4	no	—
112	C₄×C₁₃	—	2	2	no	—
113	C₄×C₁₃	—	2	2	no	—
114	C₄×C₁₃	—	2	1	no	—
115	C₄×C₁₃	—	2	1	no	—
116	C₄×C₁₃	—	8	4	no	—
117	C₂³×C₄	—	2	2	no	—
118	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
119	C₂³×C₄	C₂²⋊D₁₃	1	2	yes	—
120	C₂²×C₈	—	26	16	no	—
121	C₂²×C₈	—	26	8	no	—
122	C₂²×C₈	—	26	4	no	—
123	C₂×C₄⋊C₄	—	2	2	no	—
124	C₂×C₄⋊C₄	—	4	4	no	—
125	C₂×C₄⋊C₄	C₂×Dic₁₃	1	4	yes	—
126	C₂×C₄²	Dic₂₆	1	2	yes	—
127	C₂×C₄²	C₄×D₁₃	1	4	yes	—
128	C₂×C₄²	D₅₂	1	2	yes	—
129	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
130	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
131	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
132	#97	—	13	8	no	—
133	#97	—	26	8	no	—
134	#97	—	26	4	no	—
135	#95	—	2	4	no	—
136	#95	—	2	4	no	—
137	C₂×C₁₃	#1295	1	8	yes	complemented
138	C₂×C₁₃	C₂×#329	1	2	yes	—
139	C₂×C₁₃	C₂×#330	1	2	yes	—
140	C₂×C₁₃	C₂×#339	1	2	yes	—
141	C₂×C₁₃	C₂×#343	1	1	yes	characteristic
142	C₂⁴	C₂²⋊Dic₁₃	1	1	yes	characteristic
143	C₂²×C₄	—	2	2	no	—
144	C₂²×C₄	—	2	2	no	—
145	C₂²×C₄	—	2	8	no	—
146	C₂²×C₄	—	2	4	no	—
147	C₂²×C₄	—	4	4	no	—
148	C₂²×C₄	—	4	8	no	—
149	C₂²×C₄	C₄×Dic₁₃	1	2	yes	—
150	C₂²×C₄	#6101	1	4	yes	—
151	C₂²×C₄	C₄⋊Dic₁₃	1	2	yes	—
152	C₂²×C₄	#6103	1	4	yes	—
153	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
154	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
155	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
156	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
157	C₂×C₈	—	26	32	no	—
158	C₂×C₈	—	26	16	no	—
159	C₂×C₈	—	26	8	no	—
160	C₄⋊C₄	—	4	4	no	—
161	C₄⋊C₄	—	4	4	no	—
162	C₄²	C₄×Dic₁₃	1	2	yes	—
163	C₄²	#6101	1	4	yes	—
164	C₄²	C₄⋊Dic₁₃	1	2	yes	—
165	C₄²	#6103	1	4	yes	—
166	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
167	C₄²	C₂×C₄×D₁₃	1	2	yes	—
168	C₄²	C₂×D₅₂	1	1	yes	characteristic
169	C₁₃	C₂×#1295	1	1	yes	characteristic, complemented, Sylow
170	C₂³	#88071	1	2	yes	—
171	C₂³	#88073	1	2	yes	—
172	C₂³	#88076	1	2	yes	—
173	C₂³	#88077	1	8	yes	—
174	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
175	C₂×C₄	—	2	1	no	—
176	C₂×C₄	—	2	1	no	—
177	C₂×C₄	—	2	1	no	—
178	C₂×C₄	—	2	1	no	—
179	C₂×C₄	—	2	4	no	—
180	C₂×C₄	—	2	4	no	—
181	C₂×C₄	—	2	8	no	—
182	C₂×C₄	—	2	8	no	—
183	C₂×C₄	—	2	4	no	—
184	C₂×C₄	—	2	4	no	—
185	C₂×C₄	—	4	4	no	—
186	C₂×C₄	—	4	8	no	—
187	C₂×C₄	—	8	8	no	—
188	C₂×C₄	#88071	1	4	yes	—
189	C₂×C₄	#88071	1	2	yes	—
190	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
191	C₂×C₄	C₂×#6101	1	2	yes	—
192	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
193	C₂×C₄	C₂×#6103	1	2	yes	—
194	C₈	—	26	16	no	—
195	C₂²	#11718122	1	4	yes	—
196	C₂²	#11718124	1	8	yes	—
197	C₂²	#11718132	1	8	yes	—
198	C₂²	#11718135	1	8	yes	—
199	C₂²	C₂×#88071	1	1	yes	characteristic
200	C₂²	C₂×#88073	1	1	yes	characteristic
201	C₂²	C₂×#88076	1	1	yes	characteristic
202	C₂²	C₂×#88077	1	4	yes	—
203	C₄	—	2	2	no	—
204	C₄	—	2	4	no	—
205	C₄	—	2	2	no	—
206	C₄	—	2	2	no	—
207	C₄	—	2	1	no	—
208	C₄	—	2	1	no	—
209	C₄	—	8	4	no	—
210	C₂	#13112717	1	8	yes	direct product factor
211	C₂	C₂×#11718132	1	2	yes	—
212	C₂	C₂×#11718135	1	2	yes	—
213	C₂	C₂×#11718124	1	2	yes	—
214	C₂	C₂×#11718122	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂²⋊Dic₁₃
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₂×C₁₃×#382	C₂
socle, prime radical	C₂⁴×C₁₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₂×#382	D₁₃
hypocenter	C₁₃	C₂×#1295
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#382

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #13112717	C₂	direct (N × H)
13. C₂×#88043	C₄	semidirect
34. #88043	C₂×C₄	semidirect
137. C₂×C₁₃	#1295	semidirect
169. C₁₃	C₂×#1295	semidirect
210. C₂	#13112717	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#88043	2
#13112717	2
C₂×C₁₃×#382	2
C₂×#1295	13

Subgroups — C2×#13112717 #15752966

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13112717 #15752966